The first lockdown was sold as both preventing NHS overload, and then getting virus levels down so that a T&T system could be put in place which would allow restrictions to be slowly lifted.
What actually happened is that a T&T system was never really effective, and the slow lifting of restrictions (combined with the end of summer) eventually resulted in R>1, especially in places that had low immunity levels (the North).
It's clear now that T&T doesn't really have any effect. Is this due to Government incompetence? The answer when looking around Europe is no, because every single other country has tried the exact same thing and pretty much all have failed to prevent cases rising using their T&T system. Some like the Czech Rep (that were lauded as models of how to fight Covid) celebrated "beating the virus" in July using a contract tracing app are now being overwhelmed.
Track and trace has only really worked in places that had few cases and had a system already in place right at the start. T&T is basically impossible once a virus is widespread in the population. The asymptomatic nature of the virus also makes it many times harder to trace.
Also, there is the problem of truthfulness. Most people would admit to a tracer about going to a supermarket, but not an illicit dinner party of 8 people.
So that leaves the Government with the option of locking down for the next 6-9 months and praying for a vaccine, or keeping virus levels roughly where they are with slightly fewer restrictions and building immunity.